关键词: p-Laplacian算子, 不动点指数理论, 正解;边值问题

Abstract:

This paper deals with the p-Laplacian equation
{(φ_p(u'(t)))'+a(t)f(t, u(t))=0,      0 < t <1,

 u'(0)=u(1)=0 或 u(0)=u(1)=0
where φ_p(x)=|x|^p-2x, p > 1. By using the fixed point index theory on cones, sufficient conditions for the existence of at least two positive solutions to the boundary value problem mentioned above are established. The known results are generalized and improved.

Key words: p-Laplacian operator, Fixed point index theory, Positive solutions, Boundary value problem